Traditionally physicists thought that the smallest particles in atoms were point like, that is, they looked like points. However recently discovered evidence suggest that the smallest particle is not point like, as previously thought, but rather a vibrating string of energy. But physicists also discovered that these strings need more than three spatial dimensions to vibrate in. Particularly they need six extra spatial dimensions. In all versions of String Theory there are 10 dimensions: "Time" plus the usual three spatial dimensions x,y,z (4 dimensions, our observable universe) plus six extra spatial dimensions making a total of ten dimensions (1 time + 9 spatial = 10 dimensions).
In this animation the strings with different colors are actually vibrating in different dimensions. They do not interact with each other except gravitationally. The two dimensional membrane that they are attached to in this animation is the three dimensions that we are used to projected on 2D (for this presentation). Photons only travel on this 2D plane (again for this presentation), and this is why we cannot see them. We can only detect the strings gravitational shadow on the 2D plane. Other competing theories like M-Theory has one extra spatial dimension (making the total 11 dimensions), however this extra spatial dimension is for the description of strings themselves (whether a string is a one-dimensional object like a thread, or whether a string is a rolled up two-dimensional membrane like a tube). If the strings have thickness (or variable thickness as in this animation) then we need this 11th dimension in order to describe them (to describe the tube). However if the strings have no thickness (always unity) then there is no need for the 11th dimension. In any case, in all currently competing theories, this Dark Matter is strings vibrating in six extra spatial dimensions. And in all those theories gravity is a force carried by gravitons (just like magnetism is carried by photons). Gravitons are emitted from strings and are then absorbed by other strings even those vibrating in other dimensions (different colors in this presentation). The place where gravitons travel is called the bulk (different than the 2D plane where light travels in this presentation).
Those videos will take you from String to M-Theory: